On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid-induced velocity

Abstract

This work is an experimental study of the rise of an air bubble in still water. For the bubble diameter considered, path oscillations develop in the absence of shape oscillations and the effect of surfactants is shown to be negligible. Both the three-dimensional motion of the bubble and the velocity induced in the liquid are investigated. After the initial acceleration stage, the bubble shape remains constant and similar to an oblate ellipsoid with its symmetry axis parallel to the bubble-centre velocity, and with constant velocity magnitude. The bubble motion combines path oscillations with slow trajectory displacements. (These displacements, which consist of horizontal drift and rotation about a vertical axis, are shown to have no influence on the oscillations). The bubble dynamics involve two unstable modes which have the same frequency and are π/2 out of phase. The primary mode develops first, leading to a plane zigzag trajectory. The secondary mode then grows, causing the trajectory to progressively change into a circular helix. Liquid-velocity measurements are taken up to 150 radii behind the bubble. The nature of the liquid flow field is analysed from systematic comparisons with potential theory and direct numerical simulations. The flow is potential in front of the bubble and a long wake develops behind. The wake structure is controlled by two mechanisms: the development of a quasi-steady wake that spreads around the non-rectilinear bubble trajectory; and the wake instability that generates unsteady vortices at the bubble rear. The velocities induced by the wake vortices are small compared to the bubble velocity and, except in the near wake, the flow is controlled by the quasi-steady wake.

Force measurements on rising bubbles

“…For the size range of bubbles we study, it is has been observed in experiments and numerics that the short axis of the ellipsoidal bubble is always aligned with the bubble velocity vector [8,10,23]. A straight rising bubble therefore has Ω = 0.…”

“…Some of our force calculations depend on the shape of the bubble. It has been shown by other experimental studies that the bubble is close to an oblate ellipsoid [7,9,10]. Since we do not make such measurements, we use the experimental results of Duineveld [9] to estimate the shape of our bubbles.…”

“…While Ellingsen and Risso [10] report steady shape, de Vries et al [8] suggest that the shape of zigzagging bubbles oscillates slightly. Based on de Vries' schlieren photos, we estimate an upper limit for changes in χ to be about 10%.…”

“…These results strongly suggest that shape changes to the bubble do not play a critical role in the dynamics. Based on this result and experimental observations [10] of steady bubble shapes for the size range we study, we assume that bubble shape is fixed and use the generalized Kirchhoff equations. (We note that de Vries et al [8] report that zigzagging bubbles may have a slightly oscillating shape.…”

Visualization of gas–liquid mass transfer and wake structure of rising bubbles using pH-sensitive PLIF

“…The flow field in the wake of rising bubbles has been studied using particle image velocimetry (Brücker 1999;Lindken and Merzkirch 2000;Fujiwara et al 2004), laser doppler anemometry (Ellingsen and Risso 2001), dye visualization (Lunde and Perkins 1997) and schlieren optics (de Vries et al 2002). While these studies primarily aimed to improve the understanding of the path instabilities, the detailed mechanisms of mass transfer remain largely unclear because the spatio-temporal dynamics in the close vicinity of the bubble, i.e., the boundary layer at the interface, could not be sufficiently resolved.…”